Quartile calculator

Numbers (comma, space or newline separated)

Five number summary

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Uses the exclusive median method (Tukey's hinges) — Q1 and Q3 are the medians of the lower and upper halves, excluding the overall median itself on an odd-length list. Named here because quartile methods disagree between tools that do not say which one they use.

The five number summary

Paste or type a list of numbers, in any order and separated by commas, spaces or new lines. This sorts them and reports the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum - the standard way to describe a spread of data in five numbers instead of one average that hides how it is shaped.

Which method, and why it is named

There is more than one accepted way to compute a quartile when the list length does not split evenly, and different tools that do not say which one they use will quietly disagree with each other on the same data. This uses the exclusive median method (Tukey's hinges): the median splits the list in two, excluding the middle value itself on an odd-length list, and Q1/Q3 are the medians of each half. The method is named on the page so the number can be checked against another tool that documents its own.

Interquartile range and outliers

IQR = Q3 - Q1 is the width of the middle 50% of the data, a measure of spread that ignores extreme values rather than being dragged by them the way range (max - min) is. The standard outlier fences, Q1 - 1.5 × IQR and Q3 + 1.5 × IQR, are shown too, and any value outside them is listed - this is a convention, not a law of statistics, so borderline values are worth a second look rather than automatic exclusion.

What it needs

At least four numbers to produce a meaningful quartile split; fewer than that and the tool says so rather than returning a number computed from too little data to mean anything.